Robotic manipulator applications often require efficient online motion planning. When completing multiple tasks, sequence order and choice of goal configuration can have a drastic impact on planning performance. This is well known as the robot task sequencing problem (RTSP). Existing general purpose RTSP algorithms are susceptible to producing poor quality solutions or fail entirely when available computation time is restricted. We propose a new multi-query task sequencing method designed to operate in semi-structured environments with a combination of static and non-static obstacles. Our method intentionally trades off workspace generality for planning efficiency. Given a user-defined task space with static obstacles, we compute a subspace decomposition. The key idea is to establish approximate isometries known as $\epsilon$-Gromov-Hausdorff approximations that identify points that are close to one another in both task and configuration space. Importantly, we prove bounded suboptimality guarantees on the lengths of trajectories within these subspaces. These bounding relations further imply that trajectories within the same subspace can be smoothly concatenated which we show is useful for determining efficient task sequences. We evaluate our method with several kinematic configurations in a complex simulated environment, achieving up to 3x faster motion planning and 5x lower maximum trajectory jerk compared to baselines.

翻译：机器人操作器应用通常需要高效的在线运动规划。在完成多项任务时，序列顺序与目标构型的选择会对规划性能产生显著影响，此问题即众所周知的机器人任务序列规划问题。当可用计算时间受限时，现有的通用RTSP算法容易产生低质量解或完全失效。本文提出一种新的多查询任务序列规划方法，专为半结构化环境设计，可同时处理静态与非静态障碍物。该方法通过牺牲工作空间通用性以换取规划效率。在给定用户定义且包含静态障碍物的任务空间后，我们计算子空间分解。其核心思想是建立称为$\epsilon$-Gromov-Hausdorff近似的近似等距映射，以识别在任务空间与构型空间中均相互邻近的点。重要的是，我们证明了这些子空间内轨迹长度的有界次优性保证。这些边界关系进一步表明，同一子空间内的轨迹可平滑拼接，这被证明对确定高效任务序列具有实用价值。我们在复杂仿真环境中使用多种运动学配置评估该方法，相较于基线方法，实现了最高3倍的运动规划加速与5倍的最大轨迹加加速度降低。